A Phase 1 open label trial of intravenous administration of TAEK-VAC-HerBy vaccine in patients with advanced brachyury and/or HER2- expressing cancer. The study will be completed in 2 stages. In Stage 1 patients will be enrolled and treated according to a 3+3 dose escalation scheme. Up to 4 dose levels will be explored to determine the recommended dose of TAEK-VAC-HerBy for Stage 2 of the trial. Stage 2 will enroll either chordoma patients for treatment with TAEK-VAC-HerBy alone, or HER2- positive breast and gastric/gastroesophageal junction cancer patients for combination treatment of TAEK-VAC-HerBy vaccine and therapeutic HER2 antibodies (trastuzumab, pertuzumab). Patients in both stages will receive TAEK-VAC-HerBy intravenously, every three weeks, three administrations in total.